Continuity at Cutoff
The identifying assumption of regression discontinuity: the conditional expectations of potential outcomes are continuous in the running (forcing) variable at the treatment threshold, so units just above and just below the cutoff are comparable and the jump in outcomes at the cutoff is the causal effect. It delivers a local estimand — the effect at the cutoff (a LATE in fuzzy designs). Continuity is the weaker, nonparametric foundation; the alternative Local-Randomization framework imposes the stronger assumption that treatment is as-good-as-random within a window. It is threatened by precise sorting around the cutoff, which is probed by No-Manipulation tests.
Relied on by
RDD (the continuity-based framework); fuzzy RD combines it with the IV assumptions.